$N \leftrightarrow -N$ duality of SU(N) for stable sequences of representations
Mathematical Physics
2025-07-16 v2 High Energy Physics - Theory
math.MP
Abstract
We generalize duality of dimension formulae of representations on a (class of) representations with -dependent Young diagrams (which include the adjoint representation), and on eigenvalues of the Casimir operator for those representations. We discuss the consequences for the hypothesis of universal decomposition of powers of the adjoint representation into Casimir subspaces.
Cite
@article{arxiv.2507.10371,
title = {$N \leftrightarrow -N$ duality of SU(N) for stable sequences of representations},
author = {R. L. Mkrtchyan},
journal= {arXiv preprint arXiv:2507.10371},
year = {2025}
}
Comments
LaTeX, 12 pages, References and Acknowledgments updated